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Line Integral Convolution
In scientific visualization, line integral convolution (LIC) is a method to visualize a vector field, such as fluid motion. Features * global method * #Features#Integration-based method, integration-based method * texture-based method Convolution In signal processing this process is known as Convolution#Discrete convolution, discrete convolution. Integration-based method It is the Integral, integration-based method (technique). More precisely it is based on the discrete line integral on Regular grid, uniform grids. Discrete numerical integration is performed along a line ( more precisely curve). Line here means field line of vector field. Global method Compared to other Integral, integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt the start and end points of field lines to the specific vector field. In other words, itr shows the topol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Of The Large Magellanic Cloud ESA393163
Rotation, or spin, is the circular movement of an object around a ''axis of rotation, central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional object has an infinite number of possible central axes and rotational directions. If the rotation axis passes internally through the body's own center of mass, then the body is said to be ''autorotating'' or ''Angular momentum, spinning'', and the surface intersection of the axis can be called a ''geographical pole, pole''. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called ''revolving'' or ''orbiting'', typically when it is produced by gravity, and the ends of the rotation axis can be called the ''orbital poles''. Mathematics Mathematics, Mathematically, a rotation is a rigid body movement which, unlike a translation (geometry), translation, keeps a point fixed. This defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Calculus
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the description of electromagnetic fields, gravitational fields, and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, ''Vector Analysis''. In the conventional form using cross products, vector calculus does not generalize to higher dimensions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Function Drawing
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Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighted Arithmetic Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. Examples Basic example Given two school with 20 students, one with 30 test grades in each class as follows: :Morning class = :Afternoon class = The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terrain Cartography
Terrain cartography or relief mapping is the depiction of the shape of the surface of the Earth on a map, using one or more of several techniques that have been developed. Terrain or relief is an essential aspect of physical geography, and as such its portrayal presents a central problem in cartographic design, and more recently geographic information systems and geovisualization. Hill profiles The most ancient form of relief depiction in cartography, hill profiles are simply illustrations of mountains and hills in profile, placed as appropriate on generally small-scale (broad area of coverage) maps. They are seldom used today except as part of an "antique" styling. Physiographic illustration In 1921, A.K. Lobeck published ''A Physiographic Diagram of the United States'', using an advanced version of the hill profile technique to illustrate the distribution of landforms on a small-scale map.Lobeck, A.K. (1921''A Physiographic Diagram of the United States'' A.J. Nystrom & Co., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hann Function
The Hann function is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing. The function, with length L and amplitude 1/L, is given by: : w_0(x) \triangleq \left\. For digital signal processing, the function is sampled symmetrically (with spacing L/N and amplitude 1): : \left . \begin w = L\cdot w_0\left(\tfrac (n-N/2)\right) &= \tfrac \left - \cos \left ( \tfrac \right) \right\ &= \sin^2 \left ( \tfrac \right) \end \right \},\quad 0 \leq n \leq N, which is a sequence of N+1 samples, and N can be even or odd. (see ) It is also known as the raised cosine window, Hann filter, von Hann window, etc. Fourier transform The Fourier transform of w_0(x) is given by: :W_0(f) = \frac\frac = \frac Discrete transforms The Discrete-time Fourier transform (DTFT) of the N+1 length, time-shifted sequence is defined by a Fourier series, which also has a 3-term equivalent that is derived similarly to the Four ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Animated LIC
Animation is a method by which still figures are manipulated to appear as moving images. In traditional animation, images are drawn or painted by hand on transparent celluloid sheets to be photographed and exhibited on film. Today, most animations are made with computer-generated imagery (CGI). Computer animation can be very detailed 3D animation, while 2D computer animation (which may have the look of traditional animation) can be used for stylistic reasons, low bandwidth, or faster real-time renderings. Other common animation methods apply a stop motion technique to two- and three-dimensional objects like paper cutouts, puppets, or clay figures. A cartoon is an animated film, usually a short film, featuring an exaggerated visual style. The style takes inspiration from comic strips, often featuring anthropomorphic animals, superheroes, or the adventures of human protagonists. Especially with animals that form a natural predator/prey relationship (e.g. cats and mice, coyo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Integral Convolution Visualisation (color)
Line most often refers to: * Line (geometry), object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Podcasts * ''The Line'' (podcast), 2021 by Dan Taberski Literature * Line (comics), a term to describe a subset of comic book series by a publisher * ''Line'' (play), by Israel Horovitz, 1967 * Line (poetry), the fundamental unit of poetic composition * "Lines" (poem), an 1837 poem by Emily Brontë * ''The Line'' (memoir), by Arch and Martin Flanagan * ''The Line'' (play), by Timberlake Wertenbaker, 2009 Music Albums * ''Lines'' (The Walker Brothers album), 1976 * ''Lines'' (Pandelis Karayorgis album), 1995 * ''Lines'' (Unthanks album), 20 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Integral Convolution Visualisation
Line most often refers to: * Line (geometry) In geometry, a line is an infinitely long object with no width, depth, or curvature. Thus, lines are one-dimensional objects, though they may exist in two, three, or higher dimension spaces. The word ''line'' may also refer to a line segment ..., object with zero thickness and curvature that stretches to infinity * Telephone line, a single-user circuit on a telephone communication system Line, lines, The Line, or LINE may also refer to: Arts, entertainment, and media Films * Lines (film), ''Lines'' (film), a 2016 Greek film * The Line (2017 film), ''The Line'' (2017 film) * The Line (2009 film), ''The Line'' (2009 film) * ''The Line'', a 2009 independent film by Nancy Schwartzman Podcasts * The Line (podcast), ''The Line'' (podcast), 2021 by Dan Taberski Literature * Line (comics), a term to describe a subset of comic book series by a publisher * Line (play), ''Line'' (play), by Israel Horovitz, 1967 * Line (poetry), the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Kernel
In mathematics, an integral transform maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the ''inverse transform''. General form An integral transform is any transform ''T'' of the following form: :(Tf)(u) = \int_^ f(t)\, K(t, u)\, dt The input of this transform is a function ''f'', and the output is another function ''Tf''. An integral transform is a particular kind of mathematical operator. There are numerous useful integral transforms. Each is specified by a choice of the function K of two variables, the kernel function, integral kernel or nucleus of the transform. Some kernels have an associated ''inverse kernel'' K^( u,t ) which (roughly speaking) yields an inverse transform: :f(t) = \int_^ (Tf)(u) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution
In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reflected about the y-axis and shifted. The choice of which function is reflected and shifted before the integral does not change the integral result (see #Properties, commutativity). The integral is evaluated for all values of shift, producing the convolution function. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution (f*g) differs from cross-correlation (f \star g) only in that either or is reflected about the y-axis in convolution; thus it is a cross-c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
